Shade the Venn diagram to represent the set A' U (A ∩ B)

Slides:



Advertisements
Similar presentations
Learning Objectives for Section 7.2 Sets
Advertisements

7.5 Inclusion/Exclusion. Definition and Example- 2 sets |A  B| =|A| + |B| - |A ∩ B| Ex1: |A|=9, |B|=11, |A∩B|=5, |A  B| = ?
Chapter 7 Logic, Sets, and Counting
Shade the Venn diagram to represent the set A' U (A ∩ B)
Multiplication Principle and Addition Principle 1.Multiplication Principle: Suppose a task is accomplished by n steps and each step requires a choice from.
MATH 110 Test 2 Extra In-Class Review Problems Find n(A) if A = { 200, 201, 202, 203, …, 255 }
Section 2.3 Set Operations and Cartesian Products
Whiteboardmaths.com © 2011 All rights reserved
6.3 Basic Counting Principles In this section, we will see how set operations play an important role in counting techniques.
Chapter 7 Logic, Sets, and Counting Section 3 Basic Counting Principles.
Operations on Sets Union Intersection: Two sets are disjoint if their intersection is the null set. Difference A - B. Complement of a set A.
Applications of Venn Diagrams
Shade the Venn diagram to represent the set A' U (A ∩ B)
SETS A = {1, 3, 2, 5} n(A) = | A | = 4 Sets use “curly” brackets The number of elements in Set A is 4 Sets are denoted by Capital letters 3 is an element.
Unit 10 – Logic and Venn Diagrams
Set Theory: Using Venn Diagrams Universal Set (U): the set of all elements under consideration. #1) U = {prime.
1 Learning Objectives for Section 7.2 Sets After today’s lesson, you should be able to Identify and use set properties and set notation. Perform set operations.
Filling in a Venn diagram
Chapter 2 The Basic Concepts of Set Theory © 2008 Pearson Addison-Wesley. All rights reserved.
Introduction to Venn Diagrams SP This is a Venn diagram for two terms. We can conceive of every element of S as being within the boundary of the S circle.
Set Notation.
Sets and subsets D. K. Bhattacharya. Set It is just things grouped together with a certain property in common. Formally it is defined as a collection.
Word Problems Using Venn Diagrams
This section will discuss the symbolism and concepts of set theory
Part 1 Module 3 Survey Problems and Venn diagrams EXAMPLE A survey of 64 informed consumers revealed the following information: 45 believe that Elvis.
Venn Diagrams Numbers in each region.
Chapter 7 Sets & Probability
SORTING DATA VENN DIAGRAMS.
Chapter 2 Section 2.2 Applications of Sets. References to Various parts of a Venn Diagram The information that is told to you might not always correspond.
Topic 3: Intersection and Union
Logic and Introduction to Sets Chapter 6 Dr.Hayk Melikyan/ Department of Mathematics and CS/ Basic Counting Principles 6.3 Basic Counting.
Chapter 7 Logic, Sets, and Counting Section 2 Sets.
2.3 – Set Operations and Cartesian Products Intersection of Sets: The intersection of sets A and B is the set of elements common to both A and B. A  B.
THE NATURE OF SETS Copyright © Cengage Learning. All rights reserved. 2.
SECTION 2-3 Set Operations and Cartesian Products Slide
Chapter 2 Section 2.1 Sets and Set Operations. A set is a particular type of mathematical idea that is used to categorize or group different collections.
Section 2.3 Using Venn Diagrams to Study Set Operations Math in Our World.
Set Operations Chapter 2 Sec 3. Union What does the word mean to you? What does it mean in mathematics?
Learning Objectives for Section 7.3 Basic Counting Principles
Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you.
Quiz – last week on the month both Algebra and Geometry Algebra range – Permutation, Combinations, Systems of Linear Inequalities, Linear Programming.
Chapter 2 Sets and Functions Section 2.2 Operations on Two Sets.
Mathematics Presenter Name : Mr. Pramote Phothisai Topic : Sets Subtopic : Union of sets.
Section 1.2 – 1.3 Outline Intersection  Disjoint Sets (A  B=  ) AND Union  OR Universe The set of items that are possible for membership Venn Diagrams.
MATH 2311 Section 2.2. Sets and Venn Diagrams A set is a collection of objects. Two sets are equal if they contain the same elements. Set A is a subset.
Karen asked 20 of her friends whether they owned a cat or a dog. Seven friends owned a cat and 6 owned a dog. If 2 friends owned both a cat and a dog,
Chapter 7 Review Problems. Problem #1 Use a Venn diagram and the given information to determine the number of elements in the indicated region. n(A) =
THE NATURE OF SETS Copyright © Cengage Learning. All rights reserved. 2.
The Basic Concepts of Set Theory. Chapter 1 Set Operations and Cartesian Products.
Venn Diagrams.
6.1 Sets and Set Operations Day 2 Turn to page 276 and look at example 6.
G: SAMPLING WITH AND WITHOUT REPLACEMENT H: SETS AND VENN DIAGRAMS CH 22GH.
A Π B = all elements in both sets A and B
Venn Diagrams.
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 2.5, Slide 1 CHAPTER 2 Set Theory.
Solving Problems using Venn Diagram Mr. Albert F. Perez June 29, 2015.
Venn Diagrams EQ: How do I use a Venn diagram to represent different sets of numbers and to solve problems?
Chapter two Theory of sets
Unions and Intersections of Sets
G2.4 – Set Operations There are some operations that we can do on sets. Some of them will look very similar to operations from algebra. August 2006 Copyright.
Skipton Girls’ High School
Filling in a Venn diagram
Operations with Sets A = { 1, 2, 3 ,4, 5} B = { 2, 4, 6, 8, 10}
Chapter 7 Logic, Sets, and Counting
SETS Sets are denoted by Capital letters Sets use “curly” brackets
We will chake the answer
Chapter 7 Logic, Sets, and Counting
Presentation transcript:

Shade the Venn diagram to represent the set A' U (A ∩ B) MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) A B

Shade the Venn diagram to represent the set A' U (A ∩ B) MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) First shade 𝑨∩𝑩. A B

Shade the Venn diagram to represent the set A' U (A ∩ B) MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) First shade 𝑨∩𝑩. A B A ∩ B

Shade the Venn diagram to represent the set A' U (A ∩ B) MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) Now add in the shading for 𝑨′. A B A ∩ B

Shade the Venn diagram to represent the set A' U (A ∩ B) MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) Now add in the shading for 𝑨′. A B A ∩ B Recall that 𝐴′ is everything NOT in 𝐴.

Shade the Venn diagram to represent the set A' U (A ∩ B) MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) Now add in the shading for 𝑨′. A B A ∩ B A’ Recall that 𝐴′ is everything NOT in 𝐴.

Shade the Venn diagram to represent the set A' U (A ∩ B) MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) Now add in the shading for 𝑨′. A B A ∩ B A’ Recall that 𝐴′ is everything NOT in 𝐴. A’

Shade the Venn diagram to represent the set A' U (A ∩ B) MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) And because the remaining set operation is U (union), the final shading is the combination of the two. A B A ∩ B A’ A’

Shade the Venn diagram to represent the set A' U (A ∩ B) MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) And because the remaining set operation is U (union), the final shading is the combination of the two. A B

Shade the Venn diagram to represent the set A' U (A ∩ B) MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) A B

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ?

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter.

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last.

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′ And because the remaining set operation is ∩ (intersection), the final shading is the overlapping region (where the colors are blended).

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑟 7 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′ And because the remaining set operation is ∩ (intersection), the final shading is the overlapping region (where the colors are blended).

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑟 7 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′ And because the remaining set operation is ∩ (intersection), the final shading is the overlapping region (where the colors are blended).

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 𝑟 7 What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑟 7 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′ And because the remaining set operation is ∩ (intersection), the final shading is the overlapping region (where the colors are blended).

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 A B U

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 Begin with the innermost region. A B U

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 Begin with the innermost region. A B 13 U

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 =16 Begin with the innermost region. A B 13 3 + 𝑛 𝐴 =16 U

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 Begin with the innermost region. A B 13 3 + 𝑛 𝐴 =16 U

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 21= Begin with the innermost region. A B 13 3 + + 8 𝑛 𝐴 =16 𝑛 𝐵 =21 U

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 Begin with the innermost region. A B 13 3 + + 8 𝑛 𝐴 =16 𝑛 𝐵 =21 U

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 + 30 B A Begin with the innermost region. A B 13 3 + + 7 + 8 𝑛 𝐴 =16 𝑛 𝐵 =21 U 𝑛 𝐴′ =38

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 + 30 Begin with the innermost region. A B 13 3 + + 8 𝑛 𝐴 =16 𝑛 𝐵 =21 U 𝑛 𝐴′ =38

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 B A U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 2 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A Continue with the other interior regions. 2 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 8 9 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 8 9 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises At this point, there are still 3 that are yet to be used. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one is easiest. It tells us that there are 8 not in any of the 3 circles. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one is easiest. It tells us that there are 8 not in any of the 3 circles. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one says that there are 28 in the overlap of 𝐶′ and 𝐴. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one says that there are 28 in the overlap of 𝐶′ and 𝐴. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 The blue shaded area is 𝐶′. 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one says that there are 28 in the overlap of 𝐶′ and 𝐴. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 The yellow shaded area is 𝐴. 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one says that there are 28 in the overlap of 𝐶′ and 𝐴. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 The region of blended colors represents the A∩𝐶′. 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one says that there are 28 in the overlap of 𝐶′ and 𝐴. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 21 2 Move to the outer regions of the circles. 8 9 The region of blended colors represents the A∩𝐶′. 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 21 2 Move to the outer regions of the circles. 8 9 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one is straightforward. It tells us that there are 49 in circles A & B. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 21 2 Move to the outer regions of the circles. 8 9 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one is straightforward. It tells us that there are 49 in circles A & B. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 + Continue with the other interior regions. ? 21 = 49 + + 2 Move to the outer regions of the circles. + 8 9 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one is straightforward. It tells us that there are 49 in circles A & B. Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 Begin with the innermost region. B A 7 + Continue with the other interior regions. 2 21 = 49 + + 2 Move to the outer regions of the circles. + 8 9 10 8 U C

Find the number of elements in each region below. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(A∪B) = 49 B A 7 2 21 2 8 9 10 8 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 11 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 11 3 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 11 3 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 11 3 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 11 3 + 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 1 + 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 1 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 1 + + + 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 1 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 1 + + 19= + + + 11 3 + ? + 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 1 + + 19= + + + 11 3 + + 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B A 1 11 3 + U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B 𝑛 𝐴 =1+0+0+11 A 1 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B 𝑛 𝐴 =12 A 1 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B 𝑛 𝐴 =12 A 1 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B 𝑛 𝐴 =12 A 1 𝑛 𝐵 =0+0+0+3 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B 𝑛 𝐴 =12 A 1 𝑛 𝐵 =3 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B 𝑛 𝐴 =12 A 1 𝑛 𝐵 =3 11 3 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B 𝑛 𝐴 =12 A 1 𝑛 𝐵 =3 11 3 𝑛 𝐶 =11+0+3+4 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B 𝑛 𝐴 =12 A 1 𝑛 𝐵 =3 11 3 𝑛 𝐶 =18 4 U C

Find the number of elements in sets A, B & C if: MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ) = 3 B 𝑛 𝐴 =12 A 1 𝑛 𝐵 =3 11 3 𝑛 𝐶 =18 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 𝑛 𝐴∪𝐷 =152+133 = 285

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). ∪   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 𝐴 𝐷 111 80 31 29 10 24 152 133 𝑛 𝐴∪𝐷 =152+133 = 285

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). ∪   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 𝐴 𝐷 111 80 + + 31 29 + + 10 24 152 133 𝑛 𝐴∪𝐷 =152+133 = 285

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). ∪   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 𝐴 𝐷 285 111 80 + + 31 29 + + 10 24 152 133 𝑛 𝐴∪𝐷 =152+133 = 285

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 111 80 31 29 10 24 152 133

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 111 80 31 29 10 24 152 133

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 111 80 31 29 10 24 152 133 𝑛 𝐵∩𝐹 = 9

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 𝐵 111 54 80 𝐹 31 31 9 1 29 29 70 10 3 24 152 66 133 𝑛 𝐵∩𝐹 = 9

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 𝐵 111 111 54 80 80 𝐹 31 31 31 9 1 29 29 29 70 10 10 3 24 24 152 152 66 133 133 𝑛 𝐵∩𝐹 = 9

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 𝐵 111 111 54 80 80 𝐹 31 31 31 9 1 29 29 29 70 10 10 3 24 24 152 152 66 133 133 𝑛 𝐵∩𝐹 =9 9

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 9 𝐵 111 111 54 80 80 𝐹 31 31 31 9 1 29 29 29 70 10 10 3 24 24 152 152 66 133 133 𝑛 𝐵∩𝐹 =9 9

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F).   Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 9 𝐵 111 111 54 80 80 𝐹 31 31 31 9 1 29 29 29 70 10 10 3 24 24 152 152 66 133 133

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 Continue with the other interior regions.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 + ? Continue with the other interior regions.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 + 6 Continue with the other interior regions.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 6 Continue with the other interior regions.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 + ? 6 Continue with the other interior regions.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 + 5 6 Continue with the other interior regions.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 5 6 Continue with the other interior regions.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. ? + Begin with the innermost region. 7 5 6 Continue with the other interior regions.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 + Begin with the innermost region. 7 5 6 Continue with the other interior regions.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 Begin with the innermost region. 7 5 6 Continue with the other interior regions.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 Begin with the innermost region. 7 5 6 Continue with the other interior regions. Move to the outer regions of the circles.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 Begin with the innermost region. 7 + 5 + 6 Continue with the other interior regions. + ? Move to the outer regions of the circles.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 Begin with the innermost region. 7 + 5 + 6 Continue with the other interior regions. + 1 Move to the outer regions of the circles.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 Begin with the innermost region. 7 5 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 ? + Begin with the innermost region. + 7 5 + 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 4 + Begin with the innermost region. + 7 5 + 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 4 Begin with the innermost region. 7 5 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 ? 4 + + Begin with the innermost region. 7 + 5 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + Begin with the innermost region. 7 + 5 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 6 4 Begin with the innermost region. 7 5 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + + 7 + 5 + 6 =35 + 1

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + 92 cities were surveyed + 7 + 5 + 6 =35 + 92 1

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + 92 cities were surveyed 35 cities had at least one + 7 + 5 + 6 =35 + 92 35 1

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + 92 cities were surveyed 35 cities had at least one + 7 + 5 + 6 =35 + 92 ― 35 1 = 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + 92 cities were surveyed 35 cities had at least one + 7 + 5 + 6 + 92 ― 35 1 57 = 57 57 cities had none of these

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball Fill in the number of elements in each region. 6 6 4 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had only volleyball? 6 6 4 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had only volleyball? 6 6 4 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had only volleyball? 6 6 4 1 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer & rugby but not volleyball? 6 6 4 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer & rugby but not volleyball? 6 6 4 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer & rugby but not volleyball? 6 6 4 X 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer & rugby but not volleyball? 6 6 4 X 7 6 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer or rugby? 6 6 4 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer or rugby? 6 6 6 6 4 4 7 7 5 5 6 6 1 1 57 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer or rugby? + 6 6 6 6 + 4 4 34 + + 7 7 5 5 + 6 6 1 1 57 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer or rugby but not volleyball?

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer or rugby but not volleyball? 6 6 4 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer or rugby but not volleyball? 6 6 4 X X 7 5 X 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer or rugby but not volleyball? + 6 6 + 4 X X 7 5 X 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had soccer or rugby but not volleyball? + 6 6 + 4 X 7 16 X 5 X 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had exactly 2 teams? 6 6 4 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had exactly 2 teams? 6 6 4 7 5 6 1 57

92 cities were surveyed to determine sports teams. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball How many had exactly 2 teams? 6 6 + 4 + 7 17 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only?

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region. 8

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region. 8

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region. 8 We are told that 98 had none of the 3.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region. 8 We are told that 98 had none of the 3. 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region. 8 We are told that 98 had none of the 3. 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region. 8 We are told that 98 had none of the 3. Continue with the other interior regions. 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? ? + Begin with the innermost region. 8 We are told that 98 had none of the 3. Continue with the other interior regions. 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 + Begin with the innermost region. 8 We are told that 98 had none of the 3. Continue with the other interior regions. 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 Begin with the innermost region. 8 We are told that 98 had none of the 3. Continue with the other interior regions. 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 Begin with the innermost region. 8 We are told that 98 had none of the 3. Continue with the other interior regions. 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 At this point, is might be useful to look at what we are actually asked to find. 8 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 At this point, is might be useful to look at what we are actually asked to find. 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 99 = 26 + 8 + 65 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 99 = 26 + 8 + 65 8 So, even though we don’t know the 2 individual numbers in the green boxes, ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 99 = 26 + 8 + 65 8 So, even though we don’t know the 2 individual numbers in the green boxes, we do know now that there are 65 in that combined region. ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 65 99 = 26 + 8 + 65 8 So, even though we don’t know the 2 individual numbers in the green boxes, we do know now that there are 65 in that combined region. ? 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 65 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We also don’t have enough info to decide what goes In the two other subregions in the ‘Cat’ circle but we do know that the sum in that circle must be 76. A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 65 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We also don’t have enough info to decide what goes In the two other subregions in the ‘Cat’ circle but we do know that the sum in that circle must be 76. A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 65 76 = 26 + 8 + 42 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We also don’t have enough info to decide what goes In the two other subregions in the ‘Cat’ circle but we do know that the sum in that circle must be 76. A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 65 76 = 26 + 8 + 42 8 Using the same logic as before, we know that there are 42 in that combined region. ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We also don’t have enough info to decide what goes In the two other subregions in the ‘Cat’ circle but we do know that the sum in that circle must be 76. A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 65 42 76 = 26 + 8 + 42 8 Using the same logic as before, we know that there are 42 in that combined region. ? 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 65 42 8 ? 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 The final piece of information that we know is that there were 260 families surveyed. 65 42 8 ? 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 The final piece of information that we know is that there were 260 families surveyed. 65 42 8 ? 65 + 26 + 8 + 42 + 98 + ? = 260 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 The final piece of information that we know is that there were 260 families surveyed. 65 42 8 ? 65 + 26 + 8 + 42 + 98 + ? = 260 98 239 + ? = 260

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 The final piece of information that we know is that there were 260 families surveyed. 65 42 8 ? 65 + 26 + 8 + 42 + 98 + ? = 260 98 239 + ? = 260 ? = 21

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 The final piece of information that we know is that there were 260 families surveyed. 65 42 8 21 65 + 26 + 8 + 42 + 98 + ? = 260 98 239 + ? = 260 ? = 21

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 21 65 42 8 21 98

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet How many had a parakeet only? 26 21 65 42 8 21 98